With the increasing use of geometry scanners to create 3D models, there is a rising need for fast and robust mesh smoothing to remove inevitable noise in the measurements. While most previous work has favored diffusion-based iterative techniques for feature-preserving smoothing, we propose a radically different approach, based on robust statistics and local first-order predictors of the surface. The robustness of our local estimates allows us to derive a non-iterative feature-preserving filtering technique applicable to arbitrary "triangle soups". We demonstrate its simplicity of implementation and its efficiency, which make it an excellent solution for smoothing large, noisy, and non-manifold meshes.